Convective overstability in accretion disks: 3D linear analysis and nonlinear saturation

TL;DR

This paper confirms the existence of a hydrodynamical linear overstability in protoplanetary disks, analyzes its nonlinear saturation, and demonstrates the formation of a self-sustained 3D vortex with significant angular momentum transport.

Contribution

It provides the first 3D nonlinear analysis showing how linear overstability leads to vortex formation and angular momentum transport in accretion disks.

Findings

Linear overstability confirmed through numerical analysis.

Saturated state triggers subcritical baroclinic instability.

Formation of a self-sustained 3D vortex from linear perturbations.

Abstract

Recently, Klahr & Hubbard (2014) claimed that a hydrodynamical linear overstability exists in protoplanetary disks, powered by buoyancy in the presence of thermal relaxation. We analyse this claim, confirming it through rigorous compressible linear analysis. We model the system numerically, reproducing the linear growth rate for all cases studied. We also study the saturated properties of the overstability in the shearing box, finding that the saturated state produces finite amplitude fluctuations strong enough to trigger the subcritical baroclinic instability. Saturation leads to a fast burst of enstrophy in the box, and a large-scale vortex develops in the course of the next $\approx$100 orbits. The amount of angular momentum transport achieved is of the order of $\alpha \approx 10^{-3}$, as in compressible SBI models. For the first time, a self-sustained 3D vortex is produced from linear amplitude perturbation of a quiescent base state.